The Geometry of Point Light Source from Shadows

Shadows provide valuable information about the scene geometry, especially the whereabout of the light source. This paper investigates the geometry of point light sources and cast shadows. It is known that there is redundancy in the object-shadow correspondences. We explicitly show that no matter how many such correspondences are available, it is impossible to locate a point light source from shadows with a single view. We discuss the similarity between a point light source and a conventional pinhole camera and show that the above conclusion is in accordance to traditional camera self calibration theory. With more views, however, the light source can be located by triangulation. We proceed to solve the problem of establishing correspondences between the images of an object with extended size and its cast shadow. We prove that a supporting line, which, put simply, is a tangent line of the image regions of the object and its shadow, provides one correspondence. We give an efficient algorithm to find supporting lines and prove that at most two supporting lines can be found. The intersection of these two lines gives the direction of the point light source. All this can be done without any knowledge of the object. Experiment results using real images are shown.